A Stochastic Quasi-Newton Method for Large-Scale Optimization

TL;DR

This paper introduces a scalable and robust stochastic quasi-Newton method using limited memory BFGS updates and sub-sampled Hessian-vector products, improving large-scale optimization in machine learning.

Contribution

It proposes a novel stochastic quasi-Newton algorithm that efficiently incorporates curvature information using pointwise Hessian-vector products, enhancing robustness and scalability.

Findings

Shows promising results on machine learning problems

Demonstrates improved robustness over classical methods

Scalable to large datasets

Abstract

The question of how to incorporate curvature information in stochastic approximation methods is challenging. The direct application of classical quasi- Newton updating techniques for deterministic optimization leads to noisy curvature estimates that have harmful effects on the robustness of the iteration. In this paper, we propose a stochastic quasi-Newton method that is efficient, robust and scalable. It employs the classical BFGS update formula in its limited memory form, and is based on the observation that it is beneficial to collect curvature information pointwise, and at regular intervals, through (sub-sampled) Hessian-vector products. This technique differs from the classical approach that would compute differences of gradients, and where controlling the quality of the curvature estimates can be difficult. We present numerical results on problems arising in machine learning that suggest that the proposed method shows much promise.